diff --git a/src/mcp/__init__.py b/src/mcp/__init__.py
index 28bc4703ed..7e80516fb1 100644
--- a/src/mcp/__init__.py
+++ b/src/mcp/__init__.py
@@ -68,7 +68,12 @@
 from .client.stdio import StdioServerParameters, stdio_client
 from .server.session import ServerSession
 from .server.stdio import stdio_server
-from .shared.exceptions import MCPDeprecationWarning, MCPError, UrlElicitationRequiredError
+from .shared.exceptions import (
+    MCPDeprecationWarning,
+    MCPError,
+    SessionNotFoundError,
+    UrlElicitationRequiredError,
+)
 from .shared.uri_template import InvalidUriTemplate, UriTemplate
 
 __all__ = [
@@ -105,6 +110,7 @@
     "LoggingMessageNotification",
     "MCPDeprecationWarning",
     "MCPError",
+    "SessionNotFoundError",
     "Notification",
     "PingRequest",
     "ProgressNotification",
diff --git a/src/mcp/client/streamable_http.py b/src/mcp/client/streamable_http.py
index 053f1f10a9..cb476f4a78 100644
--- a/src/mcp/client/streamable_http.py
+++ b/src/mcp/client/streamable_http.py
@@ -40,6 +40,7 @@
     sse_within_origin,
     stream_within_origin,
 )
+from mcp.shared.exceptions import _SESSION_NOT_FOUND_MARKER
 from mcp.shared.inbound import MCP_PROTOCOL_VERSION_HEADER
 from mcp.shared.jsonrpc_dispatcher import cancelled_request_id_from_params
 from mcp.shared.message import ClientMessageMetadata, SessionMessage
@@ -406,9 +407,16 @@ async def _handle_post_request(self, ctx: RequestContext) -> None:
                             body = await response.aread()
                             parsed = jsonrpc_message_adapter.validate_json(body, by_name=False)
                             if isinstance(parsed, JSONRPCError):
+                                error = parsed.error
+                                if response.status_code == 404 and self.session_id is not None:
+                                    error = ErrorData(
+                                        code=error.code,
+                                        message=error.message,
+                                        data={_SESSION_NOT_FOUND_MARKER: True, "data": error.data},
+                                    )
                                 # The server may have set `id: null` (request rejected before its
                                 # id was parsed); use this request's id so correlation works.
-                                reply = JSONRPCError(jsonrpc="2.0", id=message.id, error=parsed.error)
+                                reply = JSONRPCError(jsonrpc="2.0", id=message.id, error=error)
                                 await ctx.read_stream_writer.send(SessionMessage(reply))
                                 return
                         except (httpx2.StreamError, ValidationError):
@@ -421,7 +429,11 @@ async def _handle_post_request(self, ctx: RequestContext) -> None:
                             # this method); "Session terminated" would be a lie here.
                             error_data = ErrorData(code=METHOD_NOT_FOUND, message="Not Found")
                         else:
-                            error_data = ErrorData(code=INVALID_REQUEST, message="Session terminated")
+                            error_data = ErrorData(
+                                code=INVALID_REQUEST,
+                                message="Session terminated",
+                                data={_SESSION_NOT_FOUND_MARKER: True},
+                            )
                     else:
                         error_data = ErrorData(code=INTERNAL_ERROR, message="Server returned an error response")
                     session_message = SessionMessage(JSONRPCError(jsonrpc="2.0", id=message.id, error=error_data))
diff --git a/src/mcp/shared/exceptions.py b/src/mcp/shared/exceptions.py
index c2a7fd44e7..ac1956be66 100644
--- a/src/mcp/shared/exceptions.py
+++ b/src/mcp/shared/exceptions.py
@@ -5,6 +5,11 @@
 from mcp_types import INVALID_REQUEST, URL_ELICITATION_REQUIRED, ElicitRequestURLParams, ErrorData, JSONRPCError
 
 
+# Internal transport marker used to preserve the distinction between a lost
+# Streamable HTTP session and an ordinary INVALID_REQUEST response.
+_SESSION_NOT_FOUND_MARKER = "__mcp_session_not_found__"
+
+
 class MCPDeprecationWarning(UserWarning):
     """A custom deprecation warning for the MCP SDK.
 
@@ -52,6 +57,10 @@ def __str__(self) -> str:
         return self.message
 
 
+class SessionNotFoundError(MCPError):
+    """Raised when a Streamable HTTP server no longer recognizes the session."""
+
+
 class NoBackChannelError(MCPError):
     """Raised when a server-initiated request has no channel that can deliver it.
 
diff --git a/src/mcp/shared/jsonrpc_dispatcher.py b/src/mcp/shared/jsonrpc_dispatcher.py
index 223373da0f..7e82f6e301 100644
--- a/src/mcp/shared/jsonrpc_dispatcher.py
+++ b/src/mcp/shared/jsonrpc_dispatcher.py
@@ -52,7 +52,12 @@
     coerce_request_id,
     run_notify_intercept,
 )
-from mcp.shared.exceptions import MCPError, NoBackChannelError
+from mcp.shared.exceptions import (
+    MCPError,
+    NoBackChannelError,
+    SessionNotFoundError,
+    _SESSION_NOT_FOUND_MARKER,
+)
 from mcp.shared.message import (
     ClientMessageMetadata,
     MessageMetadata,
@@ -458,6 +463,12 @@ async def send_raw_request(
             receive.close()
 
         if isinstance(outcome, ErrorData):
+            if isinstance(outcome.data, dict) and outcome.data.get(_SESSION_NOT_FOUND_MARKER):
+                raise SessionNotFoundError(
+                    code=outcome.code,
+                    message=outcome.message,
+                    data=outcome.data.get("data"),
+                )
             raise MCPError(code=outcome.code, message=outcome.message, data=outcome.data)
         return outcome
 
diff --git a/tests/shared/test_streamable_http.py b/tests/shared/test_streamable_http.py
index 655d9941dc..f5fd02afd7 100644
--- a/tests/shared/test_streamable_http.py
+++ b/tests/shared/test_streamable_http.py
@@ -44,7 +44,7 @@
 from starlette.routing import Mount
 from starlette.types import Message, Scope
 
-from mcp import MCPError
+from mcp import MCPError, SessionNotFoundError
 from mcp.client import ClientRequestContext, IncomingMessage
 from mcp.client.session import ClientSession
 from mcp.client.streamable_http import StreamableHTTPTransport, streamable_http_client
@@ -1140,7 +1140,7 @@ async def test_streamable_http_client_session_termination(basic_app: Starlette)
         ):
             async with ClientSession(read_stream, write_stream) as session:  # pragma: no branch
                 # Attempt to make a request after termination
-                with pytest.raises(MCPError) as exc_info:  # pragma: no branch
+                with pytest.raises(SessionNotFoundError) as exc_info:  # pragma: no branch
                     await session.list_tools()
                 assert exc_info.value.error.code == INVALID_REQUEST
                 assert exc_info.value.error.message == "Session not found"
@@ -1201,7 +1201,7 @@ async def __aexit__(self, *args: Any) -> None:
         ):
             async with ClientSession(read_stream, write_stream) as session:  # pragma: no branch
                 # Attempt to make a request after termination
-                with pytest.raises(MCPError) as exc_info:  # pragma: no branch
+                with pytest.raises(SessionNotFoundError) as exc_info:  # pragma: no branch
                     await session.list_tools()
                 assert exc_info.value.error.code == INVALID_REQUEST
                 assert exc_info.value.error.message == "Session not found"